The announcement comes just a week after JD Fortune was sacked from the group for a second time, after only performing one track on their latest album Original Sin.
Gribbin has previously provided backing vocals to Snow Patrol's Eyes Open, and also wrote Madonna's hit 'Celebration'.
The singer will join INXS for their six-date mini-tour of South America, Europe and Australia.
Gribbin told Billboard: "Without a doubt I was a fan of INXS. I remember Kick like it was yesterday.
"I remember seeing the guys on MTV and then on Jools Holland's BBC show watching as a kid, just blown away by them. INXS definitely played a huge part in my musical education as a songwriter and something I aspired to, so to be in the band now is pretty amazing."
INXS's original singer Michael Hutchence died in 1997.
> INXS announce plans for greatest hits
Watch the video for 'Pretty Vegas' by INXS below: